In typical wireless communication systems, mobile units first synchronize with a base station before data transfer may occur. A base station transmits a communication frame that includes a synchronization subframe and a data subframe. The synchronization subframe may include an acquisition sequence that includes a number of code signals which are compared to a reference signal at the mobile unit. The reference signal may be a locally generated or a stored version of the acquisition sequence. A comparison signal may be generated by comparing the received acquisition sequence and the reference signal that includes an overall correlation peak, which may then be used to determine the timing for receipt of the data portion of the communication frame.
The comparison of the received acquisition sequence and the reference signal may be determined by computing the correlation of the received acquisition sequence and the reference signal. The correlation of the two signals produces a third function that expresses the overlap of the two functions. When the received acquisition sequence and the reference signal overlap completely, the result of the correlation reaches a maximum value. For certain types of sequences, the maximum value may be a peak M times higher than any other value from an incomplete match. This peak value may be used to determine the timing offset of the communication frame between the transmitter and receiver.
To simplify calculations, the correlation of the received acquisition sequence and the reference signal may be calculated in the frequency domain instead of the time domain. Frequency domain processing has been demonstrated to provide significant savings compared to equivalent time domain processing. Convolution in the time domain is equivalent to multiplication in the frequency domain. The received acquisition sequence and the reference signal in the time domain may be converted to the frequency domain by computing a Fourier transform of the received acquisition sequence and the reverse conjugate of the reference signal. An inverse Fourier transform of the product of the Fourier transforms of the received signal and the reverse conjugate of the reference signal may then be determined to convert back to the time domain. The result may be used to determine the correlation peak in time. A Fourier transform may be calculated using a fast Fourier transform (FFT) algorithm.
One drawback of this approach is that significant hardware resources are used to compute the FFT as the acquisition sequence increases in size. Also, an amount of memory used to determine the FFT increases as the size of the acquisition sequence increases.
Accordingly, it is desired to provide low complexity, high processing gain signal acquisition methods and systems. Furthermore, desirable features and characteristics of embodiments of the inventive subject matter are apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.